In a medium bowl, whisk together eggs, oregano, salt and pepper in a medium bowl.

In a large skillet that is broiler safe, add oil and heat over medium. Add bell pepper and green onions. Stir constantly until the onions begin to wilt, about 1 minute.

Add the egg mixture into the pan. As it cooks, lift the edges of the eggs to allow the uncooked portion to go underneath. Cook about 2-5 minutes, or until the bottom is a light golden brown. Scatter the goat cheese on top and place the skillet under the broiler. Cook until puffy and golden - 2 to 3 minutes. Cool 5 minutes before cutting.